Solid State Physics Answers

Define the activity of a given radioactive substance. Calculate the activity of 1g sample
of 90Sr whose half life is 28 years. Express your answer in units of Curie (Ci). (Take
1 Ci = 3.7×1010 disintegration/s.)

Write down the wave function y211 for the hydrogen atom. Calculate the probability
current density for this state.

Write down the spectral terms for the ground states of 25Mn and 38Sr.

Consider a quantum particle confined in a well of width a. If the particle is in its ground
state calculate the quantity DxDp where ( ) 2 2 2
Dx = x − x and ( ) . 2 2 2
Dp = p − p

Obtain the expectation value of the potential energy 2 2
2
1
V (x) = mw x of the onedimensional
harmonic oscillator in the first excited state
/ 2
1/ 2
1
2 2
2
( ) 2 a x ax e
a
x −




p
y =

An electron has a deBroglie wavelength equal to that of a photon. Show that the ratio of
the kinetic energy of the electron to the energy of the photon is
hv
m c h v mc
( 2 4 + 2 2)1/ 2 − 2

The position and momentum of 1 keV electron are simultaneously measured. If the
uncertainty in its position is 1Å, calculate the uncertainty in its momentum. Mass of
electron = 9.1 10−31kg

An electron which has a kinetic energy 1.0 MeV collides with a stationary positron. (A
positron has a mass equal to an electron but the opposite charge). In the collision both
particles annihilate each other releasing two photons of equal energy which travel at an
angle of to the electron’s direction of motion. Calculate the energy, momentum and
for each photon.

How much mass does an electron gain when it is accelerated to a kinetic energy of
500 keV?

Two spaceships approach each other, each moving with the same speed as measured by a
stationary observer on the Earth. Their relative speed is 0.8c. Determine the velocities of
each spaceship as measured by the stationary observer on Earth.